LEADER 08235nam 2201741 450 001 9910817118803321 005 20210514235608.0 010 $a1-4008-5147-5 024 7 $a10.1515/9781400851478 035 $a(CKB)3710000000111092 035 $a(EBL)1642468 035 $a(OCoLC)880057790 035 $a(SSID)ssj0001258521 035 $a(PQKBManifestationID)11760678 035 $a(PQKBTitleCode)TC0001258521 035 $a(PQKBWorkID)11281443 035 $a(PQKB)11222799 035 $a(MiAaPQ)EBC1642468 035 $a(StDuBDS)EDZ0001218521 035 $a(DE-B1597)447260 035 $a(OCoLC)882259923 035 $a(OCoLC)979686369 035 $a(DE-B1597)9781400851478 035 $a(Au-PeEL)EBL1642468 035 $a(CaPaEBR)ebr10872421 035 $a(CaONFJC)MIL609617 035 $a(PPN)181789523 035 $a(EXLCZ)993710000000111092 100 $a20140528h20142014 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 00$aHodge theory /$fedited by Eduardo Cattani [and three others] ; Patrick Brosnan [and thirteen others], contributors 205 $aCourse Book 210 1$aPrinceton, New Jersey :$cPrinceton University Press,$d2014. 210 4$d©2014 215 $a1 online resource (608 p.) 225 1 $aMathematical Notes ;$v49 300 $a"Between 14 June and 2 July 2010, the Summer School on Hodge Theory and Related Topics and a related conference were hosted by the ICTP in Trieste, Italy." 311 $a0-691-16134-8 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $tFront matter --$tContributors --$tContents --$tPreface --$tChapter One. Introduction to Kähler Manifolds /$rCattani, Eduardo --$tChapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem /$rEl Zein, Fouad / Tu, Loring W. --$tChapter Three. Mixed Hodge Structures /$rZein, Fouad El / Tráng, Lê D?ng --$tChapter Four. Period Domains and Period Mappings /$rCarlson, James --$tChapter Five. The Hodge Theory of Maps /$rCataldo, Mark Andrea de / Migliorini, Luca --$tChapter Six The Hodge Theory of Maps /$rCataldo, Mark Andrea de / Migliorini, Luca --$tChapter Seven. Introduction to Variations of Hodge Structure /$rCattani, Eduardo --$tChapter Eight. Variations of Mixed Hodge Structure /$rBrosnan, Patrick / Zein, Fouad El --$tChapter Nine. Lectures on Algebraic Cycles and Chow Groups /$rMurre, Jacob --$tChapter Ten. The Spread Philosophy in the Study of Algebraic Cycles /$rGreen, Mark L. --$tChapter Eleven. Notes on Absolute Hodge Classes /$rCharles, François / Schnell, Christian --$tChapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective /$rKerr, Matt --$tBibliography --$tIndex 330 $aThis book provides a comprehensive and up-to-date introduction to Hodge theory-one of the central and most vibrant areas of contemporary mathematics-from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck's algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne's theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê D?ng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu. 410 0$aMathematical notes (Princeton University Press) ;$v49. 606 $aManifolds (Mathematics)$vCongresses 610 $aAbel?Jacobi map. 610 $aAdélic lemmas. 610 $aAlbanese kernel. 610 $aBloch?Beilinson conjecture. 610 $aChow groups. 610 $aDecomposition theorem. 610 $aDeligne cohomology. 610 $aDeligne's theorem. 610 $aGalois action. 610 $aGriffiths group. 610 $aGriffiths' period map. 610 $aGrothendieck's theorem. 610 $aHermitian structures. 610 $aHermitian symmetric domains. 610 $aHodge bundles. 610 $aHodge cycles. 610 $aHodge structure. 610 $aHodge structures. 610 $aHodge theory. 610 $aHodge-theoretic interpretations. 610 $aJacobian ideal. 610 $aKodaira?Spencer map. 610 $aKuga?Satake correspondence. 610 $aKähler manifolds. 610 $aKähler structures. 610 $aLefschetz decomposition. 610 $aPoincaré residues. 610 $aSchmid's orbit theorems. 610 $aShimura varieties. 610 $aThom?Whitney results. 610 $aTorelli theorem. 610 $aVerdier duality. 610 $aabsolute Hodge classes. 610 $aabstract variations. 610 $aalgebraic cycles. 610 $aalgebraic equivalence. 610 $aalgebraic homology. 610 $aalgebraic maps. 610 $aalgebraic varieties. 610 $aalgebraicity. 610 $aasymptotic behavior. 610 $acoherent sheaves. 610 $acohomology. 610 $acompact Kähler manifolds. 610 $acomplex manifolds. 610 $acomplex multiplication. 610 $aconjectural filtration. 610 $acontemporary mathematics. 610 $acycle class. 610 $acycle map. 610 $ade Rham cohomology. 610 $ade Rham theorem. 610 $adifferential forms. 610 $aelliptic curves. 610 $aequivalence relations. 610 $aharmonic forms. 610 $aholomorphicity. 610 $ahomological equivalence. 610 $ahorizontal distribution. 610 $ahorizontality. 610 $ahypercohomology. 610 $ahypersurfaces. 610 $aintersection cohomology complex. 610 $aintersection cohomology groups. 610 $ainvariant cycle theorem. 610 $alinear algebra. 610 $alocal systems. 610 $amixed Hodge complex. 610 $amixed Hodge structure. 610 $amixed Hodge structures. 610 $amonodromy. 610 $amorphisms. 610 $anontrivial topological constraints. 610 $anormal functions. 610 $aperiod domains. 610 $aperiod mappings. 610 $asheaf cohomology. 610 $asmooth case. 610 $asmooth projective varieties. 610 $aspectral sequences. 610 $aspread philosophy. 610 $aspreads. 610 $asymplectic structures. 610 $atangent space. 610 $atopological invariants. 610 $avariational Hodge conjecture. 610 $a?ech cohomology. 615 0$aManifolds (Mathematics) 676 $a514.223 686 $aSI 850$2rvk 700 $aCattani$b Eduardo, $0535669 702 $aCattani$b Eduardo 702 $aBrosnan$b Patrick 712 12$aSummer School on Hodge Theory and Related Topics 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817118803321 996 $aHodge theory$9922101 997 $aUNINA